There are websites out there that you can pay to be a member of, and they do the leg work for you. But with many of the mom blogs out there these days, as well as forum sites like www.afullcup.com, you can do it yourself with a little bit of time.
Buy the sunday paper with all the coupons, PLUS there are lots of places online you can go to print off coupons (and a lot of companies have Facebook pages, and they offer coupons for their products from time to time).
Using all the resources I have at hand, I match up sales with coupons to get the most possible savings. Here's an example: Next week at Meijer, the Green Giant frozen veggies are 99 cents each. They have a promotion that if you buy 3, you'll get a printed coupon for $2 off your next order. Combine that sale with a coupon that I have for $1 off of 3 boxes of GG veggies. My net total: I actually just MADE 3 cents.
Some weeks are better than others, just depends on what the sales are at the stores you shop at. But I make trips to multiple stores to get the best deals. You go prepared with your list + coupons in hand, and I'll go to stores like Meijer, Kroger, Target, Kmart, sometimes Walmart, CVS, & Walgreens.
As far as how much savings, if you work at it, you can save a LOT! For example, one of my trips to Walgreens last week, I paid at the Register $16.01 for over $50 worth of products! I really recommend joining www.afullcup.com. There is a LOT on that website, so I recommend joining, and just reading the various forums to see what you can learn. Then, you can get involved in trading coupons and other things.